Asymptotic analysis of the derivatives of the inverse error function

Diego Dominici

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arXiv · math/0607230

Asymptotic analysis of the derivatives of the inverse error function

Diego Dominici

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Abstract

The inverse of the error function, $\operatorname{inverf}(x),$ has applications in diffusion problems, chemical potentials, ultrasound imaging, etc. We analyze the derivatives $\frac{d^{n}}{dz^{n}} \operatorname*{inverf}(z) |_{z=0}$, as $n\to \infty$ using nested derivatives and a discrete ray method. We obtain a very good approximation of $\operatorname{inverf}(x)$ through a high-order Taylor expansion around $x=0$. We give numerical results showing the accuracy of our formulas.

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BibTeX RIS

Diego Dominici. 2007-06-05. Asymptotic analysis of the derivatives of the inverse error function. https://arxiv.org/abs/math/0607230

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